Generating signals for transmission of information

ABSTRACT

A method for generating a signal is presented. The method includes selecting a first set of carrier frequencies that are integral multiples of a first frequency interval, and selecting a second set of carrier frequencies that are integral multiples of a second frequency interval. The second frequency interval is an integral multiple of the first frequency interval and the second set is a subset of the first set. The method includes, for each of one or more signal carrier frequencies in the second set, selecting a plurality of associated carrier frequencies in the first set including a peak carrier frequency having substantially the same value as the signal carrier frequency, and modulating waveform frequency components at each of the selected plurality of associated carrier frequencies according to the same data value.

RELATED APPLICATION

This application is a continuation of and claims the benefit of priorityfrom U.S. application Ser. No. 11/127,401, filed May 12, 2005,incorporated herein by reference.

TECHNICAL FIELD

This invention relates to generating signals for transmission ofinformation.

BACKGROUND

Orthogonal Frequency Division Multiplexing (OFDM) is a spread spectrumtechnology in which the available bandwidth is subdivided into a numberof channels or carriers whose spectra are orthogonal to each other. Eachcarrier has a well defined peak frequency. Data are transmitted in theform of symbols that have a predetermined duration and encompass somenumber of carrier frequencies. The data transmitted on these carrierscan be modulated in amplitude and/or phase, using modulation schemessuch as Binary Phase Shift Key (BPSK), Quadrature Phase Shift Key(QPSK), or m-bit Quadrature Amplitude Modulation (m-QAM). In some cases,the spectrum of transmitted symbols is adapted to regulatoryrequirements using spectral filtering (e.g., a HAM radio band notchfilter, or an out of band roll-off filter).

SUMMARY

In a first aspect, the invention features a method for generating asignal. The method includes selecting a first set of carrier frequenciesthat are integral multiples of a first frequency interval, and selectinga second set of carrier frequencies that are integral multiples of asecond frequency interval. The second frequency interval is an integralmultiple of the first frequency interval and the second set is a subsetof the first set. The method includes, for each of one or more signalcarrier frequencies in the second set, selecting a plurality ofassociated carrier frequencies in the first set including a peak carrierfrequency having substantially the same value as the signal carrierfrequency, and modulating waveform frequency components at each of theselected plurality of associated carrier frequencies according to thesame data value.

Preferred implementations of this aspect of the invention mayincorporate one or more of the following:

The waveform frequency components include frequency samples of a Fouriertransform of an orthogonal frequency division multiplexing carrierwaveform.

The method may include generating the signal based on an inverse Fouriertransform of the modulated waveform frequency components.

The inverse Fourier transform includes a discrete inverse Fouriertransform.

Selecting the plurality of associated carrier frequencies in the firstset includes selecting carrier frequencies within a predetermineddistance from the peak carrier frequency, where the number of carrierfrequencies within the predetermined distance is fewer than the numberof the waveform frequency components used in the inverse Fouriertransform and large enough to prevent distortion in a correspondingcarrier waveform from reducing a signal-to-noise ratio of the signalbelow a predetermined threshold, where the distortion is caused bydeviation of the corresponding carrier waveform from a sinusoid.

The number of carrier frequencies within the predetermined distance issmall enough to reduce the amount of memory needed to store values usedin the inverse Fourier transform below a predetermined threshold.

The method may include tapering the signal with a pulse shaping window.

The method may include adding a cyclic prefix or postfix to the signal.

The method may include tapering the signal with a pulse shaping window.

Front and rear attenuated portions of the pulse shaping window havesubstantially the same length as the cyclic prefix or postfix.

The method may include attenuating the power spectrum of the signal atleast in part by setting amplitudes of selected waveform frequencycomponents to zero in calculating the inverse Fourier transform.

Frequencies of the selected waveform frequency components include atleast some frequencies that are in the first set but not in the secondset.

Frequencies of the selected waveform frequency components fall within afrequency band determined by transmit spectrum regulatory requirements.

The method may include selecting amplitudes of the waveform frequencycomponents at each of the selected plurality of associated carrierfrequencies according to a Fourier transform of a segment of a sinusoidat the peak carrier frequency.

The segment of the sinusoid includes an orthogonal frequency divisionmultiplexing carrier waveform.

The Fourier transform of the segment of the sinusoid is shapedapproximately as a discrete-time sinc function.

The method may include, for each of the one or more signal carrierfrequencies in the second set, combining respective associated waveformfrequency components that have the same frequency.

The data value includes a complex number.

The complex number is mapped to a binary value.

The method may include combining a plurality of symbol waveforms eachhaving a length at least as long as the inverse of the second frequencyinterval, where the combined length of the symbol waveforms is at leastas long as the inverse of the first frequency interval.

Each waveform includes an inverse Fourier transform of a set ofmodulated waveform frequency components.

In a second aspect, the invention features a method for generating asignal. The method includes selecting a first set of mutually orthogonalcarriers, and selecting a second set of mutually orthogonal carriers.The second set is a subset of the first set. The method includes, foreach of one or more signal carriers in the second set, selecting aplurality of associated carriers in the first set including a peakcarrier having substantially the same frequency as the signal carrier,and modulating each of the selected plurality of associated carriersaccording to the same data value.

Preferred implementations of this aspect of the invention mayincorporate one or more of the following:

The first and second set of mutually orthogonal carriers includeorthogonal frequency division multiplexing carriers.

The method may include generating the signal based on an inverse Fouriertransform of modulated carrier frequency components.

The method may include adding a cyclic prefix or postfix to the signal.

The method may include tapering the signal with a pulse shaping window.

The method may include attenuating the power spectrum of the signal atleast in part by setting amplitudes of selected carrier frequencycomponents to zero in calculating the inverse Fourier transform.

Frequencies of the selected carrier frequency components fall within afrequency band determined by transmit spectrum regulatory requirements.

In a third aspect, the invention features a method for generating asignal. The method includes selecting a set of mutually orthogonalcarriers, and generating a sequence of symbols based on discrete Fouriertransform frequency components. Each symbol includes a plurality of datavalues that are each encoded on a respective carrier, and each carrierincludes a plurality of frequency components.

Preferred implementations of this aspect of the invention mayincorporate one or more of the following:

The mutually orthogonal carriers include orthogonal frequency divisionmultiplexing carriers.

The method may include generating the sequence of symbols based on aninverse discrete Fourier transform of the discrete Fourier transformfrequency components.

The method may include adding a cyclic prefix or postfix to the sequenceof symbols.

The method may include tapering the sequence of symbols with a pulseshaping window.

The method may include attenuating the power spectrum of the sequence ofsymbols at least in part by setting amplitudes of selected frequencycomponents to zero in calculating the inverse discrete Fouriertransform.

Frequencies of the selected frequency components fall within a frequencyband determined by transmit spectrum regulatory requirements.

In a fourth aspect, the invention features a method for generating asignal. The method includes selecting a first set of carriers that aremutually orthogonal over a first symbol time duration, and selecting asecond set of carriers that are mutually orthogonal over a second symboltime duration. The first symbol time duration is an integral multiple ofthe second symbol time duration, and the second set is a subset of thefirst set. The method includes generating a sequence of symbols, eachsymbol including a plurality of carriers from the second set, and eachcarrier in each symbol being generated from an inverse discrete Fouriertransform of frequency components corresponding to peak frequencies ofcarriers from the first set including carriers not in the second set.

Preferred implementations of this aspect of the invention mayincorporate one or more of the following:

Each carrier in each symbol is generated from an inverse discreteFourier transform of frequency components including at least onefrequency component corresponding to a peak frequency of a carrier inthe second set and a plurality of frequency components corresponding topeak frequencies of carriers in the first set but not in the second set.

The sequence of symbols is generated from an inverse discrete Fouriertransform of frequency components representing a sum of a plurality ofsets of frequency components for a respective plurality of symbols.

Each set of frequency components includes a phase shift corresponding toa respective time shift within the first symbol time duration.

The sequence of symbols is generated from a sum of a plurality ofinverse discrete Fourier transforms of a respective plurality of sets offrequency components for a respective plurality of symbols.

The method may include modulating the frequency components to taper eachsymbol in the sequence of symbols with a pulse shaping window.

The method may include modulating the frequency components to taper thesequence of symbols with a pulse shaping window that includes front andrear attenuating portions of substantially equal length.

The method may include overlapping a first sequence of symbols with asecond of sequence of symbols by the length of the attenuating portionsand adding the overlapped portions of the sequences to generate thesignal.

In a fifth aspect, the invention features a method for generating asignal. The method includes combining a plurality of symbols to generatea plurality of waveforms. Each waveform includes a plurality of symbols,and each waveform is shaped by a first pulse shaping window thatincludes front and rear attenuating portions of substantially equallength. The method includes combining the plurality of waveformsincluding overlapping a first of the waveforms with a second of thewaveforms by the length of the attenuating portions and adding theoverlapped portions of the waveforms.

Preferred implementations of this aspect of the invention mayincorporate one or more of the following:

The overlapped portions of the waveforms represent the same symbolinformation.

The front and rear attenuating portions of the first pulse shapingwindow are shaped such that when the overlapped portions of thewaveforms are added the symbol information is restored to its form inthe unshaped waveforms.

Each symbol includes a plurality of mutually orthogonal carriers.

Each symbol is shaped by a second pulse shaping window.

The method may include generating the signal based on an inverse Fouriertransform of frequency components of the symbols, where the frequencycomponents are processed according to a Fourier transform of the secondpulse shaping window.

The method may include generating the signal based on an inverse Fouriertransform of frequency components of the symbols, wherein the frequencycomponents are processed according to time positions of symbols within awaveform.

Each waveform includes a plurality of symbols overlapped in time by anamount less than or equal to the length of an attenuating portion of thesecond pulse shaping window.

The method may include generating the signal based on an inverse Fouriertransform of frequency components of the symbols, where the frequencycomponents are processed according to a Fourier transform of the secondpulse shaping window and time positions of overlapped symbols within awaveform.

The length of the attenuating portions is at least 10% of the length ofa symbol.

The first pulse shaping window includes a raised cosine window.

Among the many advantages of the invention (some of which may beachieved only in some of its various aspects and implementations) arethe following.

Nodes of a network can support multiple modes of communication havingdifferent symbol characteristics. For example, a dual mode system cancommunicate with a legacy single mode system using one type of symbolsand with other dual mode systems using another type of symbols. The dualmode system can generate symbols of different lengths using the sameprocessing module by storing the appropriate data in one or more lookuptables.

In some implementations, in order to reduce computational complexity andoverhead, the system computes data in a symbol set by sequentiallyaddressing one carrier at a time, thereby reducing the requiredcomputational hardware as compared to a parallel implementation.

In some cases (e.g., for some high-speed embedded applications), thememory resources and/or computational resources can be reduced by usingan approximation of a carrier by reducing the representative spectraldata to only include a peak carrier frequency, plus some number ofcarrier frequencies on either side of the peak.

Other features and advantages of the invention will be found in thedetailed description, drawings, and claims.

DESCRIPTION OF DRAWINGS

FIG. 1 is a block diagram of a communication system.

FIGS. 2A-2F, 3A-3F, 4A-4F, 5A-5F, and 6A-6F are time-domain andfrequency-domain plots of OFDM symbols.

FIG. 7A is a diagram representing storage locations of carrier datavalues.

FIG. 7B is a schematic diagram of circuitry for combining carrier datavalues.

FIG. 8 is a schematic diagram of a frequency component computationalmodule.

FIG. 9A is diagram of a symbol subset waveform.

FIG. 9B is a diagram illustrating reconstruction of adjacent symbolsubset waveforms.

FIG. 10 is a flowchart of an exemplary process for generating a signal.

DETAILED DESCRIPTION

There are a great many possible implementations of the invention, toomany to describe herein. Some possible implementations that arepresently preferred are described below. It cannot be emphasized toostrongly, however, that these are descriptions of implementations of theinvention, and not descriptions of the invention, which is not limitedto the detailed implementations described in this section but isdescribed in broader terms in the claims.

System Overview

In OFDM transmission, data are transmitted in the form of OFDM“symbols.” Each symbol has a predetermined time duration or “symboltime” T_(s). Each symbol is generated from a superposition of Nsinusoidal carrier waveforms that are orthogonal to each other and formthe OFDM “carriers.” Each carrier has a peak frequency f_(i) and a phaseΦ_(i) measured from the beginning of the symbol. For each of thesemutually orthogonal carriers, a whole number of periods of thesinusoidal waveform is contained within the symbol time T_(s).Equivalently, each carrier frequency is an integral multiple of afrequency interval Δf=1/T_(s). The phases Φ_(i) and amplitudes A_(i) ofthe carrier waveforms can be independently selected (according to anappropriate modulation scheme) without affecting the orthogonality ofthe resulting modulated waveforms. The carriers occupy a frequency rangebetween frequencies f₁ and f_(N) referred to as the OFDM bandwidth.

Referring to FIG. 1, a communication system 100 includes a transmitter102 for transmitting a signal (e.g., a sequence of OFDM symbols) over acommunication medium 104 to a receiver 106. The transmitter 102 andreceiver 106 can be incorporated into nodes of a communication network(e.g., as part of a transceiver) in which each node transmits andreceives signals over the shared communication medium 104. For example,the communication medium 104 can include a power line medium that usesexisting AC wiring in a house to exchange information between nodes thatinterface with AC outlets. Due to their being designed for much lowerfrequency transmissions, AC wiring exhibits varying channelcharacteristics at the higher frequencies used for data transmission(e.g., depending on the wiring used and the actual layout). The use ofOFDM signals can improve reliability of communication in such cases dueto, for example, their resilience to narrow band interference, and theirrobustness to impulsive noise.

The communication system 100 is capable of supporting multiple modesthat have different physical (PHY) layer signaling characteristics. Suchmultiple mode operation is useful, for example, to enable coexistence ofstandard devices and legacy devices in the same network. The legacydevices may communicate using signals having a first set ofcharacteristics (called “mode A”). The upgraded standard devices maycommunicate using signals having a second set of characteristics (called“mode B”). Enabling the standard devices to communicate using eithermode A or mode B signaling facilitates the coexistence of the standardand legacy devices. Though transmitter 102 and receiver 106 areillustrated and described as supporting two modes, any number of modescan be supported.

At the transmitter 102, modules implementing the PHY layer receive aninput bit stream from a medium access control (MAC) layer. The bitstream is fed into either an encoder module 120A or an encoder module120B to perform the appropriate processing such as scrambling, errorcorrection coding and interleaving according to the mode, A or B,respectively.

The encoded bit stream is fed into a mapping module 122 that takesgroups of data bits (e.g., 1, 2, 3, 4, 6, 8, or 10 bits), depending onthe constellation used for the current symbol (e.g., a BPSK, QPSK,8-QAM, 16-QAM constellation), and maps the data value represented bythose bits onto the corresponding amplitudes of in-phase (I) andquadrature-phase (Q) components of a carrier waveform of the currentsymbol. This results in each data value being associated with acorresponding complex number C_(i)=A_(i) exp(jΦ_(i)) whose real partcorresponds to the I component and whose imaginary part corresponds tothe Q component of a carrier with peak frequency f_(i). Alternatively,any appropriate modulation scheme that associates data values tomodulated carrier waveforms can be used.

The mapping module 122 also determines which of the carrier frequenciesf₁, . . . , f_(N) within the OFDM bandwidth are used by the system 100to transmit information. For example, some carriers that areexperiencing fades can be avoided, and no information is transmitted onthose carriers. Instead, the mapping module 122 uses coherent BPSKmodulated with a binary value from the Pseudo Noise (PN) sequence forthat carrier. For some carriers (e.g., a carrier i=10) that correspondto restricted bands (e.g., an amateur radio band) no energy istransmitted on those carriers (e.g., A₁₀=0)

An inverse discrete Fourier transform (IDFT) module 124 performs themodulation of the resulting set of N complex numbers (some of which maybe zero for unused carriers) determined by the mapping module 122 onto Northogonal carrier waveforms having peak frequencies f₁, . . . , f_(N).The modulated carriers are combined by IDFT module 124 to form adiscrete time symbol waveform S(n) (for a sampling rate f_(R)), whichcan be written as

$\begin{matrix}{{S(n)} = {\sum\limits_{i = 1}^{N}{A_{i}{\exp \left\lbrack {j\left( {{2\; \pi \; i\; {n/N}} + \Phi_{i}} \right)} \right\rbrack}}}} & {{Eq}.\mspace{14mu} (1)}\end{matrix}$

where the time index n goes from 1 to N, A_(i) is the amplitude andΦ_(i) is the phase of the carrier with peak frequency f_(i)=(i/N)f_(R),and j=√−1. In some implementations, the discrete Fourier transformcorresponds to a fast Fourier transform (FFT) in which N is a power of2.

A post-processing module 126 combines a sequence of consecutive(potentially overlapping) symbols into a “symbol set” that can betransmitted as a continuous block over the communication medium 104. Thepost-processing module 126 prepends a preamble to the symbol set thatcan be used for automatic gain control (AGC) and symbol timingsynchronization. To mitigate intersymbol and intercarrier interference(e.g., due to imperfections in the system 100 and/or the communicationmedium 104) the post-processing module 126 can extend each symbol with acyclic prefix that is a copy of the last part of the symbol. Thepost-processing module 126 can also perform other functions such asapplying a pulse shaping window to subsets of symbols within the symbolset (e.g., using a raised cosine window or other type of pulse shapingwindow) and overlapping the symbol subsets, as described in more detailbelow.

An Analog Front End (AFE) module 128 couples an analog signal containinga continuous-time (e.g., low-pass filtered) version of the symbol set tothe communication medium 104. The effect of the transmission of thecontinuous-time version of the waveform S(t) over the communicationmedium 104 can be represented by convolution with a function g(τ;t)representing an impulse response of transmission over the communicationmedium. The communication medium 104 may add noise n(t), which may berandom noise and/or narrowband noise emitted by a jammer.

At the receiver 106, modules implementing the PHY layer receive a signalfrom the communication medium 104 and generate a bit stream for the MAClayer according to the mode (A or B). An AFE module 130 operates inconjunction with an Automatic Gain Control (AGC) module 132 and a timesynchronization module 134 to feed separate data paths for mode A andmode B. After synchronizing and amplifying a received symbol set usingits preamble, the receiver 106 determines which mode the symbol setcorresponds to by demodulating and decoding an initial portion of thesymbol set indicating mode A or mode B.

If mode A is detected, the receiver 106 feeds the sampled discrete-timesymbols into DFT module 136A to extract the sequence of N complexnumbers representing the encoded data values (by performing an N-pointDFT). Demodulator/Decoder module 138A maps the complex numbers onto thecorresponding bit sequences and performs the appropriate decoding of thebits (including deinterleaving and descrambling). If mode B is detected,the receiver 106 feeds the sampled discrete-time symbols into DFT module136B and Demodulator/Decoder module 138B. The sampling rate may bedifferent for mode A and mode B.

Any of the modules of the communication system 100 including modules inthe transmitter 102 or receiver 106 can be implemented in hardware,software, or a combination of hardware and software.

Multiple Mode Support

Any of a variety of techniques can be used to facilitate multiple modesupport of the transmitter 102 and the receiver 106, depending on thedifferences in symbol characteristics among the modes. To illustratesome advantages of some of these techniques, we first consider anexample in which a transmitter or receiver uses only one of mode A ormode B. For example, in one implementation, mode A corresponds to a256-point IDFT/DFT at a 50 MHz sample rate to generate and receive modeA symbols having an unextended symbol time of 5.12 μs (256 samplesspaced by 20 ns), and mode B corresponds to 3072-point IDFT/DFT with a75 MHz sample rate to generate and receive mode B symbols having anunextended symbol time of 40.96 μs (3072 samples spaced by 13.3 ns).Since mode B has a larger symbol time than mode A, the carrier frequencyspacing of mode B can be denser than the carrier frequency spacing ofmode A. Furthermore, mode B uses a 5 μs raised cosine pulse shapingwindow at the beginning and end of each symbol, while mode A uses a 0.16μs raised cosine pulse shaping window at the beginning and end of eachsymbol. These pulse shaping windows help to mitigate the spectraleffects of discontinuities between successive symbols.

In addition to these differences, there are other system performancedifferences between the modes. In mode A, a transmitter uses additionalspectral filtering of its transmit signal in order to meet a particularset of transmit spectrum requirements (e.g., HAM band notches and out ofband roll-off). The filters used for mode A can be complex and costly,and add significant distortion to the signal (some measure of distortioncompensation is attained by appropriately pre-distorting the IDFTvalues).

In mode B, with its significantly longer symbol time and its extendedraised cosine pulse shaping, the transmit spectrum can be shaped to meetthe spectral transmit requirements without necessarily requiring the useof such filters. For example, any frequencies which are zeroed in theIDFT will be highly attenuated in the transmitted power spectrum. Thisallows the transmit spectrum to be easily adapted to differentregulatory requirements.

Because of these advantages of the mode B signal characteristics, it isdesirable to implement a dual mode system that can generate mode Acompatible symbols (i.e., symbols that appear to a receiver that theywere generated by a mode A transmitter) using the mode B IDFT andextended raised cosine pulse shaping window. A technique for generatingdual mode symbols is described in the following simplified example.

Simplified Dual Mode Example

The length of the mode A and mode B symbols described above differ by afactor of 8. In this simplified example, the length of mode A and mode Bsymbols differ by a factor of 2.

Referring to FIGS. 2A-2F, an exemplary mode B OFDM symbol (FIG. 2A) hasa symbol time T_(s)=T and is composed of a first set of six carriershaving peak frequencies f₁, . . . , f₆ that are integral multiples ofthe frequency interval Δf=1/T. In this case, the carriers are evenlyspaced f₁=4Δf, f₂=5Δf, . . . , f₆=9Δf, and are combined with equalamplitudes and phases (e.g., all C_(i)=1). The positive-frequencyportion of the spectrum of the symbol in FIG. 2A is shown in FIG. 2B.FIGS. 2C and 2E show the first two carrier waveforms at frequencies f₁and f₂, respectively. FIGS. 2D and 2F show the correspondingpositive-frequency spectra of these first two carrier waveforms.

To generate the symbol in FIG. 2A, an IDFT module effectively usesdiscrete-frequency samples of the spectrum of each carrier waveform asshown in FIGS. 3D and 3F. (These frequency samples represent DFTfrequency components, and as such, extend over an entire period of aperiodic spectrum that results from the time sampling inherent in a DFTcalculation.) In this case the only nonzero frequency samples for eachcarrier are at the peak of the spectrum since the other samples fall onzeros of the carrier spectrum. The effect of this “frequency sampling”is to make the corresponding the time-domain carrier waveforms periodic,as shown in FIGS. 3C and 3E. The generated symbol is formed from oneperiod of the resulting periodic waveform shown in FIG. 3A. FIG. 3Bshows the corresponding frequency components recovered after performinga mode B DFT on samples of the transmitted symbol.

Referring to FIGS. 4A-4F, an exemplary mode A OFDM symbol (FIG. 4A) hasa symbol time T_(s)=T/2 and is composed of a second set of threecarriers having peak frequencies f₁, . . . , f₃ that are integralmultiples of the frequency interval Δf=2/T. In this case, the carriersare also evenly spaced f₁=4Δf, f₂=6Δf, f₃=8Δf, and are combined withequal amplitudes and phases (e.g., all C_(i)=1). Also, the second set ofcarriers is a subset of the first set of carriers. Thepositive-frequency portion of the spectrum of the symbol in FIG. 4A isshown in FIG. 4B. FIGS. 4C and 4E show the first two carrier waveformsat frequencies f₁ and f₂, respectively. FIGS. 4D and 4F show thecorresponding positive-frequency spectra of these first two carrierwaveforms.

To generate the symbol in FIG. 4A, an IDFT module still usesdiscrete-frequency samples of the spectrum of each carrier waveform asshown in FIGS. 5D and 5F, but in this case the mode A samples are spacedfurther apart than the mode B samples by a factor of 2 (since the symboltime of the mode A symbols is shorter than the symbol time of the mode Bsymbols by a factor of 2). However, there is still only one nonzerofrequency sample for each carrier at the peak of its spectrum since theother samples fall on zeros of the carrier spectrum. This frequencysampling results in the periodic carrier waveforms shown in FIGS. 5C and5E. The generated symbol corresponds to one period of the resultingperiodic waveform shown in FIG. 5A. FIG. 5B shows the correspondingfrequency components recovered after performing a mode A DFT on samplesof the transmitted symbol.

FIGS. 6A-6F show exemplary waveforms and frequency sampled spectra for asystem supporting dual mode symbol generation. The system can generate amode B OFDM symbol as described above with reference to FIGS. 2A-2F andFIGS. 3A-3F. The system can also generate a mode A compatible OFDMsymbol (FIG. 6A) that contains a shorter mode A symbol with length T/2within the longer mode B symbol time T_(s)=T. This mode A compatiblesymbol is composed of the second set of three carriers having peakfrequencies f₁=4Δf, f₂=6Δf, f₃=8Δf, that are integral multiples of thefrequency interval Δf=2/T.

To generate the mode A compatible symbol corresponding to one period ofthe periodic waveform shown in FIG. 6A, the IDFT module 124 usesdiscrete-frequency samples of the spectrum of each carrier waveform asshown in FIGS. 6D and 6F at the denser mode B frequency spacing. Thisfrequency sampling results in the periodic carrier waveforms shown inFIGS. 6C and 6E. FIG. 6B shows the corresponding frequency componentsrecovered by a receiver expecting a mode A symbol and performing a modeA DFT on samples of the transmitted symbol.

In this case, more than one of the frequency samples of each carrierspectrum is nonzero. In fact, nonzero samples can extend over an entireperiod of the DFT spectrum. In a practical system it is sufficient torepresent only a finite number of samples on either side of the peaksince the magnitudes of the samples become smaller away from the peak.This is because the shape of the carrier spectrum is approximately thatof a “sinc” function (i.e., sinc(x)=sin(7πx)/(7πx)). (The illustratedpositive-frequency carrier spectrum actually corresponds to the sum oftwo sinc functions centered at the positive and negative carrierfrequency peak values.)

In this dual mode case as in the other cases in this simplified example,the carriers are combined with equal amplitudes and phases (e.g., allC_(i)=1), but in general the amplitudes and phases are modulatedaccording to a respective data value. In this dual mode case, since eachmode A carrier corresponds to multiple nonzero frequency samples, eachof which is also a mode B carrier frequency, multiple waveformcomponents are modulated according to the same data value, as describedin more detail below. In addition to modulating the multiple componentsaccording to a data value, the components can be multiplied by a complexphase shift to move the T/2 length symbol to any position within the Tlength symbol (since a phase shift in the frequency domain correspondsto a time shift in the time domain). Other transformations can beperformed on the symbols as well. For example, a pulse shaping windowcan be applied in the frequency domain by multiplying each component byan appropriate complex number (e.g., a DFT of a discrete time pulseshaping window).

In the DFT and IDFT calculations, the time domain is discrete as well,however, as long as the time sampling rate is large enough (e.g., leasttwice as large as the largest carrier frequency) the effect on theillustrated time-domain and frequency-domain representations is minimal.

Constructing Symbol Sets

Since the length in time of the mode B symbol is larger than the lengthin time of a mode A symbol (e.g., by a factor of 8 for the 5.12 μs longmode A symbols and 40.96 μs long mode B symbols described above),multiple mode A symbols can be sent in a time slot used by a mode Bsymbol. Thus in this example, a symbol set that normally includes 4 modeB symbols can include, for example, 32 mode A symbols.

In one implementation, the system generates a portion of a symbol setincluding multiple shorter mode A symbols by a process that includes:calculating the appropriate complex number C_(i) for each mode B carrierfrequency f_(i) in a set of mode B carriers used to represent a mode Acarrier, optionally applying an equivalent frequency domainrepresentation of any symbol transformations being performed (e.g., aFourier transform of a pulse shaping window if one is being used), andadding the resulting complex numbers from different carriers and/orsymbols that use the same mode B carrier frequency index i. These valuesare calculated and stored for subsequent use in the IDFT module 124.First we describe the generation of the individual mode A symbols, thenthe generation of the symbol set.

Symbol Generation

In a first implementation, a process for generating a mode A symbol usesa “full spectrum” representation of each mode A carrier using all DFTvalues (or “frequency samples” corresponding to the more densely spacedmode B carrier frequencies). Data values are then modulated onto eachmode A carrier by multiplying its respective DFT values with theappropriate complex number (determined by the data value and themodulation approach). The DFT values that are being modulated areoptionally pre-processed based on the frequency domain representation ofany pulse shaping and overlapping as described below. The IDFT of theresulting DFT values is calculated. The result of this IDFT is a timedomain waveform where each mode A carrier of each mode A symbol of thesymbol set is modulated by its respective data value.

For mode B symbols, the system 100 uses mode B carriers that are spacedin frequency at ⅛ the distance of the mode A carriers. Therefore, thenumber of mode B carriers needed to generate a full spectrumrepresentation of a mode A symbol (assuming 76 mode A carriers are used)is approximately: 76 mode A carriers*8 mode B carriers per mode Acarrier=608 mode B carriers. Assuming a symbol set of 5 symbols, theresulting memory requirements would be as follows.

Memory Per mode A carrier=608 complex words/carrier

Memory Per mode A symbol=608 complex words/carrier*76 mode Acarriers=46,208 complex words/symbol

Memory Per Symbol Set=46,208 complex words/symbol*5 symbols=231,040complex words

In some cases (e.g., for some high-speed embedded applications), thememory resources and/or computational resources used in this examplemake a second implementation discussed below, which greatly reduces thememory and processing resources, more appropriate.

As described above, the largest values of the mode A carrier spectrumare at the peak frequency and at the adjacent and nearby frequencies.Based on this observation, an approximation of a mode A carrier can beobtained by reducing the representative spectral data to only includethe peak carrier frequency, plus some number of mode B carrierfrequencies on either side of the peak. As would be expected, the moremode B carriers that are used to represent the mode A carrier, the moreaccurate the representation of the mode A carrier in the mode A symbol.Listed below are two examples which show the tradeoff between DFT datasize and waveform distortion.

1) 15 total mode B carriers used to represent each mode A carrier yielda 22 dB signal-to-noise ratio (SNR) at the mode A receiver. This SNR issufficient for QPSK modulation.

2) 39 total mode B carriers used to represent each mode A carrier yielda 30 dB SNR at the mode A receiver. This SNR is sufficient for 256-QAMmodulation.

The resultant memory requirements for each of the above examples areshown below.

1) 15 total mode B carriers used to represent each mode A carrier:

Memory Per mode A carrier=15 complex words/carrier

Memory Per mode A symbol=15 complex words/carrier*76 mode Acarriers=1,140 complex words/symbol

Memory Per Symbol Set=1,140 complex words/symbol*5 symbols=5,700 complexwords

2) 39 total mode B carriers used to represent each mode A carrier:

Memory Per mode A carrier=39 complex words/carrier

Memory Per mode A symbol=39 complex words/carrier*76 mode Acarriers=2,964 complex words/symbol

Memory Per Symbol Set=2,964 complex words/symbol*5 symbols=14,820complex words

As can be seen from the above examples, using a subset of the mode Bcarriers to represent each mode A carrier can attain a significantreduction in required memory.

However, if this implementation is to be made practical for embeddedreal-time applications, not only should the memory resources used bereduced, but so should the computational resources. Explained below is amethod for modulating (multiplying) and summing the mode A carrierinformation in a way that reduces resulting computational resources.

In some implementations, in order to reduce computational complexity andoverhead, the system 100 computes the mode B symbol set data bysequentially addressing one mode B carrier at a time, thereby reducingthe required computational hardware as compared to a parallelimplementation. Since the mode B carriers have a frequency spacing thatis ⅛th the pitch of the mode A carriers, if each mode A carrier is to berepresented by a spectrum that has 9 or more mode B carriers, then themode A carrier spectra will overlap in the frequency domain. If the modeA carrier spectra are to be constructed in such a way that theirfrequency components are addressed (indexed) by the using acorresponding mode B carrier number, then multiple lookup tables (or theequivalent thereof) will be needed in order to distinguish the frequencycomponents that overlap in frequency. In some implementations, the modeB carrier data values stored in the lookup table not only represent thefrequency components of a mode A carrier, but also include effects ofthe shorter mode A pulse shaping window, and a time shift including theoption of overlapping a mode A symbol carrier waveform in time withadjacent mode A symbol carriers.

FIG. 7A shows an example in which each mode A carrier is represented by15 total mode B carriers. A storage module accessible by the IDFT module124 stores the lookup tables for accessing carrier data values indexedby peak frequency. In this example, frequency-indexed lookup tablestorage locations are shown with respect to a common frequency axis 700for a first lookup table 701 of carrier data values stored in a firstROM and a second lookup table 702 of carrier data values stored in asecond ROM (e.g., read-only memories (ROMs) addressed by a numberrepresenting the mode B peak carrier frequency). These ROMs provide twolookup tables in order to access the overlapping (in frequency) carrierdata values for each mode A carrier spectrum. This example shows 4 modeA carriers, with mode B carrier data values for the two mode A carriers1 and 3 stored in the first ROM, and mode B carrier data values for thetwo mode A carriers 2 and 4 stored in the second ROM. Other storagearrangements are possible. For example, a single ROM can store bothlookup tables in separate address spaces.

Each of these 4 mode A carriers is associated with 15 mode B carriers(including the mode B carrier with the same frequency as the peak and 7on either side of the peak). These mode B carriers represent thefrequency components of a mode A carrier. Each of the corresponding 15frequency components is multiplied by the same modulating data value.The 7 frequency components of the first mode A carrier that overlap with7 frequency components of the second mode A carrier are then added, andlikewise for the 7 overlapping components of the second and third, andthird and fourth mode A carriers.

While it is possible to perform these multiply and add functions inparallel, a great deal of computational hardware would be required torealize such an implementation. In order to reduce the hardwarerequirements, some implementations perform these operations one mode Bcarrier at a time, thus reducing the required computational hardware.

For example, referring to FIG. 7B, circuitry 710 indexes frequencycomponents in each of the respective ROMs (indexed by mode B carriernumber) and multiplies each frequency component by its correspondingmodulating data value, and then adds the resulting modulated values fromthe ROMs that have the same mode B carrier number. This example uses 15mode B carriers to represent each mode A carrier and therefore uses 2separate ROMs to store overlapping spectral data. If additional mode Bcarriers were used to represent each mode A carrier, additional ROMswould be used to store the overlapping frequency components. The numberof ROMs (or lookup tables) used can be determined by the followingformula.

Number of Tables=floor((Number of mode B carriers−1)/8)+1

where, “Number of mode B carriers” is and odd number.

For this example of 15 mode B carriers:

Number of Tables=floor((15−1)/8)+1=2

For the case of 39 mode B carriers:

Number of Tables=floor((39−1)/8)+1=5

Symbol Set Generation

A symbol set that is to be transmitted within a signal over thecommunication medium 104 may be constructed from shorter mode A symbols,longer mode B symbols, or a combination of mode A and mode B symbols, asdescribed above. To attain the spectral performance inherent in thelonger the longer mode B symbols, multiple (e.g., 4) mode A symbols canfirst be combined into a “symbol subset”, and then multiple symbolsubsets can be combined into a symbol set using the same processesand/or circuitry used to combine mode B symbols into a symbol set. Thesymbol subsets can also include a symbol fragment to prevent the longermode B pulse shaping window from distorting the mode A symbols.

After the frequency components at a given mode B carrier index have beensummed over different carriers in a mode A symbol (as shown in FIG. 7B),the frequency components at a given mode B carrier index should besummed over different mode A symbols in a symbol subset. FIG. 8 shows anexemplary frequency component computational module 800 included in theIDFT module 124 to perform these summations. The module 800 includes 4adders and sequentially steps through the mode B carrier numbers. Theresulting symbol subset includes 4 complete mode A symbols and a 5^(th)symbol fragment that represents the portion of a symbol from a previoussymbol subset that is attenuated by a pulse shaping window, as describedin more detail below.

After the system 100 has computed and stored the final frequencycomponent (DFT) value, the IDFT module 124 uses these values to generatea symbol subset waveform shown in FIG. 9A. This symbol subset generationprocess is repeated as needed. If the number of mode A symbols to betransmitted in a symbol set is not a multiple of 4, the final symbolsubset includes only the necessary number of symbols to complete asymbol set. The symbol subset is shaped based on the position of itslast symbol, using the terminal symbol pulse shaping technique describedbelow.

Alternative implementations are possible. For example, in someimplementations, the IDFT module 124 generates a waveform for eachsymbol and adds the respective waveforms to yield a symbol subset.

Pulse Shaping

A symbol set can include two types of pulse shaping: the shorter mode Apulse shaping window applied to individual mode A symbols within asymbol subset, and the longer mode B pulse shaping window applied toboth the mode B symbols and the symbol subsets within the symbol set. Asdescribed above, the mode A windowing function can be applied to eachmode A symbol in the frequency domain.

The longer mode B pulse shaping window is used in some implementationsto achieve a desired spectral performance. However, when the pulseshaping window is applied to the ends of the mode A symbol subset, themode A symbols that have been shaped may be so highly shaped that theyare rendered unusable. When a symbol subset is shaped, the first andlast samples of length WINDOW_SIZE (typically 384 samples) areattenuated by an appropriate pulse shaping window. If the attenuatingportion of the pulse shaping window (of length WINDOW_SIZE) is notnegligible compared to the length of a mode A symbol (e.g., 5%, 20%,50%, or more of a mode A symbol), then this pulse shaping causessignificant signal attenuation to the mode A symbol, however, itseffects can be compensated for using the following pulse shapingtechnique.

Referring to FIG. 9A, the first symbol 902 of the symbol subsetgenerated by the IDFT module 124 is a symbol fragment of lengthWINDOW_SIZE, and its stored DFT values correspond to the lastWINDOW_SIZE waveform values of an unmodulated mode A symbol. This symbolfragment 902 is then modulated by the same data used to modulate thelast symbol of the previous symbol subset, and is attenuated by thefront portion of the pulse shaping window. The last symbol 904 of thesymbol subset is attenuated by the rear portion of the pulse shapingwindow. As with the mode A pulse shaping, this mode B pulse shaping maybe applied in the time domain, or alternatively may be applied in thefrequency domain.

When symbol subsets are concatenated into a symbol set for transmission,the current symbol subset is overlapped with the previous symbol subsetby amount WINDOW_SIZE and the overlapped waveform values are addedtogether. The result is that the attenuated mode A symbols are fullyreconstructed between adjacent symbol subsets as shown in FIG. 9B.

At the front of the symbol set, the attenuated mode A symbol fragmentcarries redundant preamble information. This information is used toreconstruct the pulse shaped portion of the preamble using the overlapmethod described above. If the last mode A symbol to be transmitted ispositioned as the last (i.e., fourth) symbol of the final symbol subset,the final symbol subset waveform is extended with a cyclic postfix oflength WINDOW_SIZE, and the rear portion of the windowing function isapplied to the postfix, thereby preserving the full amplitude of thelast mode A symbol. If the last mode A symbol occurs at any otherlocation in the final symbol set, the attenuation window is appliedimmediately following the end of the last mode A symbol. Using thesemethods, the unwanted attenuation effects of the pulse shaping windoware removed allowing the transmission of contiguous and spectrallycorrect mode A compatible symbols.

FIG. 10 shows a flowchart of an exemplary process 1000 for generating asignal. The process 1000 selects (1002) a first set of carrierfrequencies that are integral multiples of a first frequency interval.The process 1000 selects (1004) a second set of carrier frequencies thatare integral multiples of a second frequency interval, where the secondfrequency interval is an integral multiple of the first frequencyinterval and the second set is a subset of the first set. For each ofone or more signal carrier frequencies in the second set, the process1000 selects (1006) a plurality of associated carrier frequencies in thefirst set including a peak carrier frequency that is substantially thesame as the signal carrier frequency, and modulates (1008) waveformfrequency components at each of the selected plurality of associatedcarrier frequencies according to the same data value. The process 1000generates (1010) the signal based on an inverse Fourier transform of themodulated waveform frequency components. Selecting the plurality ofassociated carrier frequencies in the first set comprises selectingcarrier frequencies within a predetermined distance from the peakcarrier frequency, where the number of carrier frequencies within thepredetermined distance is fewer than the number of the waveformfrequency components used in the inverse Fourier transform and largeenough to prevent distortion in a corresponding carrier waveform fromreducing a signal-to-noise ratio of the signal below a predeterminedthreshold, where the distortion is caused by deviation of thecorresponding carrier waveform from a sinusoid.

Many other implementations other than those described above are withinthe invention, which is defined by the following claims.

1. A method for generating a signal, the method comprising: selecting afirst set of carrier frequencies that are integral multiples of a firstfrequency interval; selecting a second set of carrier frequencies thatare integral multiples of a second frequency interval, where the secondfrequency interval is an integral multiple of the first frequencyinterval and the second set is a subset of the first set; and for eachof one or more signal carrier frequencies in the second set, selecting aplurality of associated carrier frequencies in the first set including apeak carrier frequency that is substantially the same as the signalcarrier frequency; and modulating waveform frequency components at eachof the selected plurality of associated carrier frequencies according tothe same data value.
 2. The method of claim 1, wherein the waveformfrequency components comprise frequency samples of a Fourier transformof an orthogonal frequency division multiplexing carrier waveform. 3.The method of claim 1, further comprising generating the signal based onan inverse Fourier transform of the modulated waveform frequencycomponents.
 4. The method of claim 3, wherein the inverse Fouriertransform comprises a discrete inverse Fourier transform.
 5. The methodof claim 3, further comprising tapering the signal with a pulse shapingwindow.
 6. The method of claim 3, further comprising adding a cyclicprefix or postfix to the signal.
 7. The method of claim 6, furthercomprising tapering the signal with a pulse shaping window.
 8. Themethod of claim 7, wherein front and rear attenuated portions of thepulse shaping window have substantially the same length as the cyclicprefix or postfix.
 9. The method of claim 3, further comprisingattenuating the power spectrum of the signal at least in part by settingamplitudes of selected waveform frequency components to zero incalculating the inverse Fourier transform.
 10. The method of claim 9,wherein frequencies of the selected waveform frequency componentscomprise at least some frequencies that are in the first set but not inthe second set.
 11. The method of claim 9, wherein frequencies of theselected waveform frequency components fall within a frequency banddetermined by transmit spectrum regulatory requirements.
 12. The methodof claim 1, further comprising selecting amplitudes of the waveformfrequency components at each of the selected plurality of associatedcarrier frequencies according to a Fourier transform of a segment of asinusoid at the peak carrier frequency.
 13. The method of claim 12,wherein the segment of the sinusoid comprises an orthogonal frequencydivision multiplexing carrier waveform.
 14. The method of claim 12,wherein the Fourier transform of the segment of the sinusoid is shapedapproximately as a discrete-time sinc function.
 15. The method of claim1, further comprising, for each of the one or more signal carrierfrequencies in the second set, combining respective associated waveformfrequency components that have the same frequency.
 16. The method ofclaim 1, wherein the data value comprises a complex number.
 17. Themethod of claim 16, wherein the complex number is mapped to a binaryvalue.
 18. The method of claim 1, further comprising combining aplurality of symbol waveforms each having a length at least as long asthe inverse of the second frequency interval, where the combined lengthof the symbol waveforms is at least as long as the inverse of the firstfrequency interval.
 19. The method of claim 18, wherein each waveformcomprises an inverse Fourier transform of a set of modulated waveformfrequency components.